Is this fiction, exactly? Abe Ravelstein, the brilliant, self-mocking, high-living, ever-opinionated hero of Saul Bellow's new work, has asked the narrator, Chick, a favour. "I'd like you to write me up after I'm gone." As Bellow let it be known long before the book was published, Ravelstein memorialises his friend and mentor Allan Bloom, and the request was Bloom's.

Bellow's novels have often been rooted in memoir - most strikingly, his sad comedy Humboldt's Gift (1974) was based on his recollections of doomed poet and alcoholic Delmore Schwartz. But this is something more. "I'm laying this on you as an obligation," Ravelstein tells the hesitant narrator. Here is the obligation's fulfilment.

Bloom, who died in 1992, was a Chicago professor who became famous, or notorious, with his surprise bestseller The Closing of the American Mind (1987). This elegant conservative polemic, with an introduction by Bellow, argued that Disney and Derrida had done for liberal culture in America.

Higher education in the humanities taught the young to find reflected in books merely their own senses of grievance or self-worth, and put anything difficult off limits. "The popular success of his book drove the academics mad," writes Chick. It also enabled his friend to fund his expansive enjoyment of life, caught in a series of vivid, half-ludicrous vignettes. Thanks to a book saying that students should learn Ancient Greek, he can now stay in a Paris hotel in the suite next to Michael Jackson's.

The appeal to Bellow of Ravelstein's extravagance and excitement is characteristic: the "big-souled" intellectual meeting up with the material world is the situation of most Bellow comedy. Ravelstein, whose hands tremble over small tasks with "a tremendous eager energy that shook him when it was discharged", tips the strongest French coffee down the most expensive jacket in Paris. He wants to be stylish, but his enthusiasm trips him up. He sets himself to lecture, but keeps turning to gossip. His wisdom is taken for wisecracks. Bellow may have lifted the details from his observation of Bloom, but they belong happily in a novel, and Ravelstein is the latest in his long line of flamboyant sages.

Bellow's hero (and it is obvious that Bloom truly was Bellow's hero) is as large and vociferous as life, full of appetites and arguments. "Ravelstein, with his bald, powerful head, was at ease with large statements, big issues and famous men, with decades, eras, centuries." An intellectual millionaire, enjoying the trappings of belated wealth, he is an overpowering presence, and a wrestler rather than a guru. "I was not about to get in the ring with this Sumo champion representing Platonic metaphysics," says Chick, as he ducks one of the intellectual debates that Ravelstein likes to provoke.

Obituaries of Bloom were silent about his sexuality: not so Bellow. Ravelstein is dying of Aids, but finding death "such a weird aphrodisiac"; still cruising, still paying off the rent boys. Though he is dead when the novel begins, we keep returning to his life and its last months - his time "in the end-zone". "When he coughed you heard the sump at the bottom of a mine-shaft echoing." He is brought alive unsentimentally by the energy of Bellow's still-inventive prose, with its mixtures of the elevated and the brutally jokey. Chatty and improvisatory, it is still thick with mostly unacknowledged quotation and misquotation (the pleasures of allusion for those who have read the great books that Bloom pressed on Americans).

Even more than Bellow's other novels, its narrative is structureless, digressive, almost whimsical. It circles around the character - the sayings and the idiosyncrasies - of its protagonist. When it loses him it loses its way, and its other main characters are pale. Ravelstein's lover, Nikki, is a silent functionary. The narrator's - ie Bellow's - wife is too good, and too often complimented, to have any life at all, though Bellow does a characteristically sardonic turn with his ex-wife (an astrophysicist in life and in this book). A serene lunar presence in Bellow's eloquently sombre novel The Dean's December (1982), her cold delicacy is now cruelly portrayed. As ever, these great male American novelists, with all those marriages behind them, cannot help putting their ex-wives in their books.

Intriguingly, Bellow cannot even do his own dramas of the soul without Ravelstein to reflect them. This, his first full-length work for 14 years, produced in his mid-80s, is much drawn to death, yet the personal element is curiously flat. The narrator's account of his own near-death experience after an exotic form of food-poisoning (based closely on Bellow's own recent brush with the reaper) seems pointless and utterly without drama: mere autobiographical data, unchanged into fiction.

Bellow needs his Ravelstein, his re-imagined version of his friend, to look at death in the face. He may be doing his duty to Allan Bloom, but he is also, by the quality of his writing rather than any weight of ideas, winning a fictional space to talk of last things - to wonder unabashed about the hungers of "the soul" while biology sucks at the narrator and at his favourite character. "We don't easily give up a creature like Ravelstein to death." Such not-giving-up is what this novel manages, by an achievement of style as much as of affection: a character is saved from death. An effort of fiction-making after all.